FIGS. 10 and 11 show an example of a focusing error detection device for an optical head such as shown in Japanese Patent Application Laid-open No. 93223/1977 or J. M. Braat and G. Bouwhuis, "Position Sensing In Video Disc Read Out", Applied Optics, vol. 17, No.13, p.p. 2013-2021, (1978).
In FIG. 10, 1 depicts a light source such as a He-Ne laser and 2 is an auxiliary lens for expanding a diameter of light beam emitted by the light source 1. 3 depicts an information recording medium such as an optical disk, 4 an information recording plane of the information recording medium 3 and 5 an information track, the information recording medium 3 being rotatable around a rotary shaft 6. 7 depicts a half mirror for separating irradiation light to the information recording medium 3 from reflection light from the information recording medium 3, 8 a mirror for bending an optical path of the irradiation light to the information recording medium 3, and 9 an objective lens for focusing the irradiation light from the light source 1 onto the information track 5. 10 depicts a focusing error detection sensor which is composed of a plurality of optical detecting elements. 11 depicts an auxiliary lens for projecting an image formed on an exit pupil of the objective lens 9 by a reflection light from the information recording medium 3 onto the optical detecting elements in the focusing error detecting sensor 10. In FIG. 10, an image of a point a on the exit pulpil of the objective lens 9 is formed on the focusing error detecting sensor 10 as a point a' by the auxiliary lens 11.
In FIGS. 11, 12 and 13 depict the optical detecting elements in the focusing error detecting sensor, 14 a subtractor for providing a difference between output signals from the optical detecting elements 12 and 13, 15 an adder for adding the output signals of the detecting elements 12 and 13, 16 a phase shifter for shifting a phase of an output signal of the adder 15 by 90.degree., 17 a multiplier for multiplying an output of the phase shifter 16 with the output signal of the subtractor 14, and 18 a low pass filter for passing a low frequency component of the output signal of the multiplier.
The operational principle of this focusing error detecting device is based on the fact that, in reading an information on the information recording plane 4 which acts as a diffraction grating, there is produced a phase difference between 0 order light directly reflected by the information recording medium and the first order diffraction light reflected and diffracted by information pits on an information track thereof and the phase difference corresponds to a focusing error. The phase difference between the 0 order light and the first order diffraction light can be measured by analysing interference fringes in an interference region of the 0 order light and the first order diffraction light in a plane remote enough from the information recording medium, that is, a plane in which the 0 order light and the first order diffraction light can be observed with an enough distance therebetween (the latter plane will be referred to hereinafter as a plane disposed in a "far field" of the information recording medium) and, in the conventional device, a focusing error signal is produced by electrically processing outputs of a plurality of optical detecting elements arranged in the far field.
A coordinate system necessary to describe an operation of this conventional device will be defined firstly. As shown in FIG. 10, .xi. and .eta. axes are set on the information recording plane 4 of the information recording medium 3 in parallel with a center line of the information track 5 and orthogonally of the center line, respectively. The exit pupil plane of the objective lens 9 which focuses light beam onto the information recording medium 3 is referred to as XY plane, with an origin of the XY plane being made coincident with a center of the exit pupil plane and an X axis being made in parallel with the .eta. axis. An entrance pupil plane of the objective lens 9 in which reflection light is fallen is set as an X'Y' plane which is the same plane as the XY plane.
An amplitude distribution on the entrance pupil plane of the objective lens 9 formed by reflection light from the information recording medium 3 is equal to an amplitude distribution on the exit pupil plane of the objective lens 9 existing on the opposite side to the information recording plane and is projected on the optical sensor 10 by the auxiliary lens 11. Therefore, the intensity distribution of light in the far field formed by the reflection light from the information recording medium 3 can be observed on the optical sensor 10. FIG. 12 shows a correspondency of the above mentioned coordinate system. For these real coordinates X, Y, .xi., .eta., X' and Y', normalized coordinates x, y, u, v, x' and y' are defined as follows: EQU x=X/R, y=Y/R (1) EQU u=.xi./(.lambda./NA), v=.eta./(.lambda./NA) (2) EQU x'=X'/R, y'=Y'/R (3)
where R is a radius of aperture of the objective lens 9, NA is a numercal aperture of the objective lens 9 and .lambda. is wavelength of the light source 1.
Now, a mathematical treatment of the information recording plane will be described. (cf. G. Bouwhuis et al, "Principles of Optical Disc Systems", Adam Hilger, p.p. 24-30, (1985))
Looking at an information recording plane of an optical video disc or compact disc, it is found that a plurality of information tracks are arranged on the plane equidistantly (1.6-1.7 .mu.m gap). This means that such disc is a diffraction grating having a single spatial frequency with respect to a direction orthogonal to the information tracks. As to a direction parallel with the information tracks, an information is recorded by changing pit position, pit period and pit length etc. Therefore, spatial frequency spectrum in a direction parallel with the information tracks is not single but broadened considerably. However, in a case of optical video disc, since a video signal which is frequency modulated is recorded in the form of pulse width modulated, it is possible to consider that spatial frequency in a direction parallel with the information tracks is constant locally and the spatial frequency does not change non-continuously. Therefore, in the case of the optical video disc, it is possible to consider the information recording plane as a two dimensional diffraction grating as shown in FIG. 13.
In FIG. 13, 21 depicts information pit which, in the case of the optical video disc, is a land or recess having a physical depth in the order of 0.1 .mu.m compared with a peripheral portion thereof. Representing a period in the track direction (.xi. axis) of the information recording plane and a period in the direction (.eta. axis direction) perpendicular to the information track by P and Q, respectively, periods p and q for the normalized coordinates u and v shown in FIG. 13 become as follows: EQU p=P/(.lambda./NA), q=Q/(.lambda./NA) (4)
Since it is possible to consider that the information recording plane having the above mentioned structure provides a light beam incident on the information pit portion a phase delay .phi.s proportional to the depth of the pit, an amplitude reflectivity Ro (u,v) can be represented by ##EQU1## Since Ro(u,v) is a periodic function both in u and v directions, it can be Fourier-expanded as follows: ##EQU2## The reflection light amplutude distribution A.sub.D (x',y') on the focusing error detecting optical sensor 10, which is significant for the focusing error detection, can be represented as follow when Rm,n is used. (cf. G. Bouwhuis et al, "Principles of Optical Disc Systems", Adam Hilger, p.p. 24-30, (1985)) ##EQU3## where u.sub.0 is an amount of movement of the information recording medium in the track direction in the normalized coordinates, v.sub.o is a deviation of track in the direction perpendicular to the track and a(x,y) is irradiation light amplitude distribution on the exit pupil of the objective lens, i.e., pupil function.
It is now considered reflection light intensity distribution on the focusing error sensor 10 when the information recording plane 4 is deviated from a focus point of a focusing beam from the objective lens 9 to the latter by .DELTA.f as shown in FIG. 14.
A wavefront aberration coefficient W.sub.20 of off-focusing corresponding to the off-focus .DELTA.f is given by EQU W.sub.20 =NA.DELTA.f/2.lambda. (9)
(cf. G. Bouwhuis et al, "Principles of Optical Disc Systems", Adam Hilger, p. 41, (1985)). Therefore, when it is assumed that an optical system from the light source 1 to the information recording plane 4 is aberration free, the irradiation light amplitude distribution a(x,y) on the objective lens can be represented by ##EQU4##
The optical detecting elements 12 and 13 have rectangular light receiving surfaces such as shown in FIGS. 11 or 15, respectively, the longitudinal direction thereof being transversal to the information track 5, i.e., in parallel with the y' axis. Further, since the elements 12 and 13 are arranged in an interference region of the (0,0) order reflection light and the (1,0) order reflected and diffracted light, the amplitude distribution A.sub.D1 (x', y') of reflection light from the information recording medium 3 on the optical sensor can be represented by using the equation (8) as follows: EQU A.sub.D1 (x',y')=Ro,o.multidot.a(-x', -y')+R.sub.1,o.multidot.exp(-2.pi.i u.sub.o /p).multidot.a(-x'+1/p, -y') (11)
In this expression, (m,n) order diffraction light means, among light components of light reflected and diffracted by the information recording medium acting as the two dimensional diffraction grating, diffraction light having diffraction order of m order in the track direction and n order in the direction perpendicular thereto. For example, among light beams emanating from the center (x=0, y=0) of the exit pupil of the objective lens 9, a component thereof which is subjected to the (m,n) order diffraction can reach a point (x'=m/p', y'=n/q) on the optical sensor. Representing a magnitude difference between Fourier coefficients Ro,o ans R.sub.1,o by .alpha. and a phase difference therebetween by .psi..sub.0, EQU R.sub.1,o=.alpha..multidot.e.sup.i.psi.0 Ro,o (12)
is established. By using the equation 11 in the equation 12, A.sub.D1 (x',y') can be written as EQU A.sub.D1 (x',y')=Ro,o(a(-x', -y')+.alpha..multidot.e.sup.i.psi.0 exp(-2.pi.i u.sub.0 /p).multidot.a(-x'+1/p, -y')) (13)
When it is assumed that the amplitude distribution of irradiation light on the exit pupil of the objective lens is constant and EQU .tau.(x,y)=1 (14)
A.sub.D1 (x',y') can be represented by using the equation 10 in the equation 13 as follow. ##EQU5## Since, when the information recording medium 3 is rotating around the rotary shaft 6 at a line speed So in the normalized coordinate u, the following equation is established EQU U.sub.o =S.sub.o .multidot.t (17)
the equation 16 can be rewritten as follow: EQU .vertline.A.sub.D1 (',y').vertline..sup.2 =.vertline.Ro,o.vertline..sup.2 [(1+.alpha..sup.2)+2.sub..alpha. cos (.psi..sub.0 -2.sub..pi. s.sub.0 t/p+2.pi.W.sub.20 (-2x'/p+1/p.sup.2))] (18)
The meaning of the equation 18 is as follow:
(1) There is produced interference fringes in a region of the optical sensor surface disposed in the far field of the information recording medium, where (0,0) order reflection light and (1,0) order reflection and diffraction light overlap each other.
(2) The spatial period of interference fringes is inversely proportional to wavefront aberration coefficient W.sub.20. That is, The spatial frequency of interference fringe is proportional to W.sub.20.
(3) Interference fringes vary, with time, at an angular frequency .omega. (=2.pi. So/p) determined by a ratio between a period p in the information track direction and a line speed So in the same direction.
Therefore, interference fringes observed on the optical sensor surface can be said as a traveling wave propagating along the x' axis, which has a period varying depending upon an amount of W.sub.20, i.e., off-focusing .DELTA.f and a traveling direction depending upon a sign of W.sub.20.
In the conventional device as shown in FIGS. 10 and 11, W.sub.20, i.e., off-focusing .DELTA.f, is detected as to be described. Firstly, with the center positions of the respective detecting elements 12 and 13 being x.sub.1 -.DELTA.x/2 and x.sub.1 +.DELTA.x/2, respectively as shown in FIGS. 11 or 15, output currents I.sub.D1 and I.sub.D2 of the elements 12 and 13 become as follows according to the equation 18: ##EQU6## where I.sub.1 =K(1+.alpha..sup.2) and I.sub.2 =K.multidot.2.alpha.. A difference signal I.sub.DF and a sum signal I.sub.SUM of the elements 12 and 13, which are derived from the subtractor 14 and the adder 15, respectively, are written as follows: ##EQU7## Since, when the off-focusing is not considerably large, the following equation is established EQU W.sub.20 .DELTA.x/p&lt;&lt;1 (22)
the equations 20 and 21 can be simplified as follows, respectively: EQU I.sub.DF =2I.sub.2 .multidot.2.pi.W.sub.20 .DELTA.x/p.multidot.sin (.psi..sub.0 -.omega.t+2.pi.W.sub.20 (-2x.sub.1 /p+1/p.sup.2))(23) EQU I.sub.SUM =2I.sub.1 +2I.sub.2 .multidot.cos (.psi..sub.0 -.omega.t+2.pi.W.sub.20 (-2x.sub.1 /p+1p.sup.2)) (24)
Then, the output I.sub.SUM of the adder is supplied to the phase shifter 16 to obtain a signal I.sub.R the phase of a.c. component of which is advanced by 90.degree. and which is represented by EQU I.sub.R =2I.sub.2 .multidot.sin (.psi..sub.0 -.omega.t+2.pi.W.sub.20 (-2x.sub.1 /p+1/p.sup.2)) (25)
and, in the multiplier 17, I.sub.R and I.sub.DF are multiplied with each other to obtain a signal S.sub.M which is as follow: ##EQU8## Finally, a focusing error signal Sf is obtained by passing the Signal S.sub.M through the low pass filter 18 capable of passing signal component whose angular frequency is smaller than 2.omega., which is as follow: EQU Sf=2I.sub.2.sup.2 .multidot.2.pi.W.sub.20 .DELTA.x/p (27)
Since the signal Sf is an odd function of the wavefront aberration coefficient W.sub.20, i.e., the amount of off-focusing .DELTA.f, it can be used to correct the focusing according to the known method.
In the conventional focusing error detection device, the focusing error signal is produced by a synchronous detection of the difference signal from the two optical detecting elements with using the sum signal thereof as a reference signal. Therefore, both of the difference signal and the sum signal must be single frequency signals variable with time. This means that it requires, in the information recording medium, a constant spatial frequency in a direction parallel with the information track. Therefore, since it is impossible for some information recording medium such as the compact disc in which information is recorded by modulating it to the pit length and the pit gap to derive single frequency signal to be used as the reference signal, it is impossible to produce the focusing error signal.
Further, even for an information recording medium such as the magneto-optical disc which has a continuous guide groove and in which there is no information recorded in the form of phase pit or amplitude pit in a direction parallel with information tracks, it is impossible to produce a focusing error signal by the conventional focusing error detection device.